Seen the show (entirely thanks to my sister, actually), so I get what you're talking about. I'd argue that the show has characters that seem to have inversely proportional IQs to Emotional IQs. Seems like in the show the higher your EIQ is, the lower your IQ is, and vice-versa.
For a very, very narrow definition of IQ (focusing around math/science/etc. aptitude, which that show seems to focus on from your descriptions), I've found that to be true in real life as well: people very far off in that kind of intelligence tend to have trouble relating to people who can't make the same kinds of mental leaps that they can, and (in some cases, particularly around aspergers/autism) have trouble understanding that other people don't think in the same terms, or at the same levels, that they do. Thus, low EIQ.
IQ was originally to measure logic and pattern recognition. Used for that, it does a fairly good job. I've taken professional "IQ" tests that had several different sections that tried to measure different areas, and I can see those being reasonably valid as well. Of course, the tests were three hours or so with a trained observer taking notes, not multiple-choice tests on the internet. No multiple choice at all, if I remember correctly, and no math/grammar/general knowledge questions either.
That said, the idea of IQ, EIQ, etc. are kind of bogus. I'm a programmer, good at math and logic. My brother is poor at math, excellent at linguistics and music. How can you even compare those two skill sets and their underlying natural aptitude? Some people are good at thinking about certain kinds of problems (how to make a program to do X), some people are good at thinking about other kinds of problems (what notes will sound good together?), nobody short of brain damage/development issues is bad at thinking about all kinds of problems, and it's all modified by mood, persistence, focus, competing interests, and outside stimuli. Trying to generate a single number to encompass all of that is not only pointless, but misleading.
And that said, and not to derail the thread, but I wonder how many DF players are (officially | self-diagnosed) out in the abnormal range of the autism spectrum?